System, Method, and Computer-Readable Medium for Multilevel Shaping for Wireless Communication Systems

1. A method of wireless communication, the method comprising: determining a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the order of the types and an integer; determining an element of the determined type from one or more elements of the determined type, wherein the elements of the determined type are ordered and each is uniquely associated with a vector having the counts of symbols of the alphabet associated with the determined type and wherein the element is determined based on the order of the elements and the integer; and transmitting a communications signal representing the determined element.

2. The method of claim 1 , wherein the plurality of types are ordered based on a shaping gain to minimize an average energy.

3. The method of claim 1 , wherein determining the element comprises determining the element based on the order of the elements and a residue integer based on the integer and the determined type.

4. The method of claim 1 , wherein the alphabet comprises a number of symbols (M), wherein M is not equal to 2 N , wherein N is any integer.

5. The method of claim 1 , wherein the integer comprises a plurality of bits for encoding.

6. The method of claim 1 , wherein the determined element comprises a plurality of the symbols, and wherein transmitting the signal comprises transmitting the plurality of symbols.

7. A computer-readable medium having computer-executable instructions for execution by a processing system, the computer-executable instructions for wireless communication, comprising: instructions for determining a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the order of the types and an integer; instructions for determining an element of the determined type from one or more elements of the determined type, wherein the elements of the determined type are ordered and each is uniquely associated with a vector having the counts of symbols of the alphabet associated with the determined type and wherein the element is determined based on the order of the elements and the integer; and instructions for transmitting a communications signal representing the determined element.

8. An apparatus for wireless communication, the apparatus comprising: means for determining a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the order of the types and an integer; means for determining an element of the determined type from one or more elements of the determined type, wherein the elements of the determined type are ordered and each is uniquely associated with a vector having the counts of symbols of the alphabet associated with the determined type and wherein the element is determined based on the order of the elements and the integer; and means for transmitting a signal representing the determined element.

9. An apparatus for wireless communication, the apparatus comprising: a processing system configured to: determine a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the order of the types and an integer; and determine an element of the determined type from one or more elements of the determined type, wherein the elements of the determined type are ordered and each is uniquely associated with a vector having the counts of symbols of the alphabet associated with the determined type and wherein the element is determined based on the order of the elements and the integer; and a transmitter configured to transmit a communication signal representing the determined element.

10. The device of claim 9 , wherein the plurality of types are ordered to minimize an average energy.

11. The device of claim 9 , wherein the processing system determines the element based on the order of the elements and a residue integer based on the integer and the determined type.

12. The device of claim 9 , wherein the alphabet comprises a number of symbols (M), wherein M is not equal to 2 N , wherein N is any integer.

13. A media player comprising: at least one antenna; a processing system configured to: determine a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the order of the types and an integer; and determine an element of the determined type from one or more elements of the determined type, wherein the elements of the determined type are ordered and each is uniquely associated with a vector having the counts of symbols of the alphabet associated with the determined type and wherein the element is determined based on the order of the elements and the integer; and a transmitter configured to transmit, via the at least one antenna, a communication signal representing the determined element.

14. A method of wireless communication, the method comprising: receiving a communications signal representing a vector; determining a type from a plurality of types based on the communications signal, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the vector; and determining an integer based on the vector and the determined type.

15. The method of claim 14 , wherein the plurality of types are ordered based on a shaping gain to minimize an average energy.

16. The method of claim 14 , wherein determining the integer comprises determining the integer based on an order of elements associated the determined type.

17. The method of claim 14 , wherein the alphabet comprises a number of symbols (M), wherein M is not equal to 2 N , wherein N is any integer.

18. A computer-readable medium having computer-executable instructions for execution by a processing system, the computer-executable instructions for wireless communication, comprising: instructions for receiving a communications signal representing a vector; instructions for determining a type from a plurality of types based on the communications signal, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the vector; and instructions for determining an integer based on the vector and the determined type.

19. An apparatus for wireless communication, the apparatus comprising: means for receiving a communications signal representing a vector; means for determining a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the vector; and means for determining an integer based on the vector and the determined type.

20. An apparatus fix wireless communication, the apparatus comprising: a receiver configured to receive a communication signal representing a vector; and a processing system configured to: determine a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the vector; and determine an integer based on the vector and the determined type.

21. The apparatus of claim 20 , wherein the plurality of types are ordered to minimize an average energy.

22. The apparatus of claim 20 , wherein the processor determines the integer based on an order of elements associated the determined type.

23. The apparatus of claim 20 , wherein the alphabet comprises a number of symbols (M), wherein M is not equal to 2 N , wherein N is any integer.

24. A television comprising: at least one antenna; a receiver configured to receive a communication signal representing a vector via the at least one antenna; and a processing system configured to: determine a type from a plurality of types, wherein the plurality of types are ordered and each is uniquely associated with counts of symbols of an alphabet and wherein the determined type is based on the vector; and determine an integer based on the vector and the determined type.

25. A method of wireless communication, comprising: determining a type from a plurality of types based at least in part on a plurality of bits, wherein each type of the plurality of types comprises one or more vectors, each of the one or more vectors including one or more elements of an alphabet, wherein counts of the elements in the vectors are unique for each type; determining a vector from the one or more vectors of the determined type based at least in part on the plurality of bits; mapping the elements of the determined vector onto a signal constellation; and transmitting a wireless signal based on the mapped elements.

26. The method of 25 , wherein the plurality of types are ordered and wherein the vectors of each type are ordered, wherein determining the type comprises determining type based on the plurality of bits and the order of the types, and wherein determining the vector comprises: determining the vector based on the plurality of bits and the order of vectors in the determined type.

27. The method of claim 25 , wherein the plurality of bits comprise a number of bits k plus a number of bits n, wherein the k bits are used to determine the type and the vector, and wherein the mapping comprises mapping each element of the determined vector to a signal in the constellation having a sign determined by a respective one of the n bits.

28. The method of claim 25 , wherein the plurality of bits comprise a number of bits k plus a number of bits m, wherein the k bits are used to determine the type and the vector, and wherein the mapping comprises mapping each element of the determined vector to a signal in a coset of the constellation, wherein the coset is determined using the m bits.